Referring to FIG. 1, the behavior of light at a reflecting surface of a substrate 10 can be described as either specular reflection 12 or diffuse (also called Lambertian) reflection 14. In specular reflection, the rays of an incident bundle of light rays 16 all reflect from a smooth surface of the substrate 10 at an angle .beta. equal to their respective angles of incidence .alpha. (Snell's Law). For example, a mirror is a reflecting surface that exhibits substantially specular reflection. By contrast, in diffuse reflection 14, the majority of the rays of an incident bundle of light rays 18 reflect from the surface of the substrate 10 at respective angles not equal to their respective original angles of incidence .alpha..
Traditional "depth-from-defocus" apparatus includes the apparatus described in a paper entitled "Real-Time Focus Range Sensor", presented and distributed by Nayar, Watanabe, and Noguchi at the International Conference on Computer Vision (ICCV95), Nov. 30, 1994, and in M. Watanabe, S. K. Nayar, and M. Noguchi, "Real-time Computation of depth from defocus". Proc. of the SPIE, vol 2599:A-03, p.14-25, November 1995. This apparatus is part of a system that uses light reflected from an illuminated surface to determine the depth of the features of an object. However, such "depth-from-defocus" systems do not always correctly determine the depth of the specular features of an object. This is due in part because depth-from-defocus apparatus typically include crossed polarizers to "cut out" or substantially attenuate specular reflections.
Typically, crossed polarizers, i.e., polarizers rotated 90 degrees with respect to each other, attenuate specular reflections by more than 90%. This degree of attenuation effectively prevents light reflected from specular object features from reaching the image sensor, and consequently, results in the loss of depth information conveyed by light reflected from the specular object features. For this reason, traditional depth-from-defocus apparatus is restricted to imaging objects having surfaces that exhibit entirely diffuse reflection, such as clay pots, cardboard models, and styrofoam cups, as presented in Watanabe, Nayar, and Noguchi; "Real-time computation of depth from defocus" Proc. of the SPIE, vol 2599:A-03, p.14-25, November 1995.
Thus, to obtain three-dimensional images of entirely specular objects, such as a mirror-like structure on a silicon wafer, or objects exhibiting both specular and diffuse reflection such as a solder joint on a circuit board, another approach to obtaining depth information from defocus effects must be used.